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JEE Main Math Class 12 Inverse Trigonometric Functions Questions
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© examsnet.com
Question : 19
Total: 74
Let
x
=
sin
(
2
tan
−
1
α
)
and
y
=
sin
(
1
2
tan
−
1
4
3
)
. If
S
=
{
a
∈
R
:
y
2
=
1
−
x
}
, then
∑
α
∈
S
16
α
3
is equal to
[25-Jul-2022-Shift-2]
Your Answer:
Validate
Solution:
∵
x
=
sin
(
2
tan
−
1
α
)
=
2
α
1
+
α
2
.
.
.
.
.
.
(i)
and
y
=
sin
(
1
2
tan
−
1
4
3
)
=
sin
(
sin
−
1
1
√
5
)
=
1
√
5
Now,
y
2
=
1
−
x
1
5
=
1
−
2
α
1
+
α
2
⇒
1
+
α
2
=
5
+
5
α
2
−
10
α
⇒
2
α
2
−
5
α
+
2
=
0
∴
α
=
2
,
1
2
∴
∑
α
∈
S
16
α
3
=
16
×
2
3
+
16
×
1
2
3
=
130
© examsnet.com
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